# Why does a boat lean into its turn?

1. Oct 23, 2009

### nautikal

When cars turn they lean away from the turn as the torque from the centripetal force is balanced by the larger normal force on the tires on the outside of the turn. However, boats lean into their turns. So when a boat is turning left, it will lean to left. This doesn't make any sense to me.

When a boat is turning to the left, the centripetal force is from the water and is applied on the lower portion of the boat and towards the left (assume a typical small craft that is hydroplaned and that we are viewing the boat from the stern). This is therefore a clockwise torque (again when looking from at the stern of the boat).

There is also the clockwise torque as a result of the imbalance in buoyant force when the boat leans to port.

The only counterclockwise torque I can think of in this situation is from the weight vector, which is generally above the waterline and thus a counterclockwise torque. But what initially causes the boat to lean into the turn?

2. Oct 23, 2009

### A.T.

What about the torque from the rudder? To turn left it diverts the water to the left. This creates a torque around the vertical axis (which turns the boat left) but also a torque around the long axis which leans the boat to the left.

Last edited: Oct 23, 2009
3. Oct 23, 2009

### rcgldr

A conventional single hull boat leans in to the turn because the rudder/prop/jet exerts a sideways force onto the water below the center of mass of the boat, coexistant with the water applying an equal and opposing force, causing the boat to lean inwards.

In the case of a sailboat with a tall mast, the momentum of the mast may cause the boat to lean outwards.

Last edited: Oct 23, 2009
4. Oct 23, 2009

### sophiecentaur

When the boat turns, if is in displacement mode (not a hovercraft or hydrofoil) the outer side of the hull will be pushing against the water as it rotates about a vertical axis. This would have two effects - there will be a centripetal force, causing it to follow a curved path and a vertical force, due to upthrust from the displaced water, on the outer side, causing it to rise. These two will occur without the need for a rudder or steerable propellor (outboard engine). You could tow the boat and get both effects.
You can't get a hovercraft to turn using the water: it will just keep sliding in a straight line unless you can displace some water or push hard with the prop.

The idea about the effect of a mast doesn't seem to work for me because, at least with a keel boat, the heavy keel will also be 'thrown outwards' (sorry but it's the easiest way to describe it) and cause the mast to lean in because the same moments situation should apply as in the static case. Btw my mast is only 65kg (c.m. at 6m above the water) and the keels are about 1tonne each (c.m. about 0.7m below): it has to stay up un a high wind hitting the sails). The moments are very much 'in favour' of the keels. The situation with a centreboard dinghy may be different but the mast, despite being tall, is probably an equally small fraction of the mass of boat plus crew.
However, dinghys can do funny things when turning quickly but they are only traveling fast when the sail is up and that seriously complicates things!.